Sunday, September 20, 2015

It really cracks me up how religious people with no biology training think they have some special insight into evolution that the people who actually study biology somehow haven't figured out.

Granville Sewell, William Dembski, Barry Arrington --- the list goes on and on. And here's another name to add to the list: Steve Laufmann. It shouldn't surprise you that this dolt is published by the Discovery Institute, a group whose fundamental purpose is to confuse the public about evolution.

Laufmann, who claims to be an expert in "information systems", but cannot seem to manage to complete his own web page (check out all the "lorem ipsums" under "The Blog"), has absolutely nothing new to say. It's all the usual claims without evidence, like "Random events cannot create complex information, except in two circumstances: (a) there is some predefined notion of a desirable outcome, and (b) any "positive gains" toward that outcome are protected from random degradation through some external mechanism. Both of these special circumstances require intention, which the physical laws cannot offer." Laufmann clearly doesn't know a damn thing about information, since random events are, in fact, essentially the only source of information, and it doesn't require anything like "a predefined notion of a desirable outcome".

Oh, and if you had any doubts that Laufmann's doubts are based in religion, check out this page, where he is described as a "long-time ministry leader".

Saturday, September 19, 2015

Here's a postcard showing the lobby of the Philadelphia Record newspaper building. The card seems to be postmarked 1945, which suggests this photo is from the time that my parents worked there as newspaper reporters. (The couple at the right center even looks a little like them!)

Wednesday, September 09, 2015

Wow, has it been a year already? A year ago, I wrote to the illustrious Robert Marks II, asking him about a claim he made: "we all agree that a picture of Mount Rushmore with the busts of four US Presidents contains more information than a picture of Mount Fuji".

Monday, September 07, 2015

Here we have the amusing spectacle of Denyse O'Leary offering nothing truthful at all, with regard to speciation.

What is a "species" anyway? If you listen to Darwinblather, you’d never think to ask.

Right you are, Denyse! If evolutionary biologists studied speciation, there would be articles and books about it in the scientific literature, written by prominent Darwinists (and even some philosophers!). But of course, there are no such things. (Don't follow those links, Denyse!)

In short, no one knows.

In short, Denyse doesn't know. I can guarantee she never read Coyne's book.

As you know, I'm very skeptical about the ability of most philosophers to say anything interesting (or even true) about science. Here is yet another example of bad philosophy, this time from James Barham.

Really, I wish anyone who wants to prattle on and on about the deficiencies of Darwinism would take, at the very least, undergraduate courses on the theory of computation and artificial intelligence. It would save a lot of electrons being wasted the way Barham does.

It starts badly, with a claim that the "Darwinian consensus" (whatever that means) is "gradual[ly] crumbling" and that the "official explanation" (no kidding -- like a 9/11 truther, he really says that) "of the nature of living things---and therefore of human beings---that we've all been led to believe in for the past 60 or 70 years turns out to be dead wrong in some essential respects."

Yeah, yeah. We've heard that for more than a hundred years; it's what Glenn Morton called the "longest-running falsehood in creationism".

"The machine metaphor was a mistake---organisms are not machines, they are intelligent agents."

This is precisely the kind of silliness that a good course on the theory of computation could avoid. Why does he think that a machine cannot be an "intelligent agent"?

"For one thing, it [Darwinism] meant that all purpose is an illusion, even in ourselves, which is absurd. We know that is not true from the direct evidence of our own experience."

No, the biological theory of evolution does not mean that "all purpose is an illusion". Trouble results from using the vague word "purpose", which means many things to different people. It is not a concept that has a precise scientific definition (what are the units of "purpose"?), although Barham tries to provide one: he says, "Purpose is the idea that something happens, not because it must tout court, according to physical law, but rather because it must conditionally, in order for something else to happen." Well, that's not what most people mean by purpose, but even so, practically any computer program would exhibit purpose under Barham's definition. And nature is filled with objects that can serve as a basis for computation, including DNA and sandpiles. There is simply no logical barrier at all to computing devices arising through natural processes.

There are a few philosophers who have something interesting to say about evolution, but Barham is not one of them.

Sunday, September 06, 2015

The International Journal of Mathematics Research, also known as IJMR, is officially a Silly Journal™. Here's why:

Reason #1: The journal's URL, as provided on some papers they have published, is given incorrectly: it says "http://www.ripublication.com/ijmr.htm",
but the correct URL is "http://www.ripublication.com/irph/ijmr.htm". You have to be particularly incompetent to run a journal which cannot publish its own URL correctly.

Reason #2: The journal's listing of their editorial board contains spelling errors, lists at least one editor twice, and contains not a single person in the countries where mathematics research is strongest (e.g., USA, Canada, France, Germany, Netherlands, UK, Russia, Italy, Australia). Also, no e-mail for any of the editors is given.

Reason #3: Recently they published this paper: Ali Abtan, "A New Theorem for the Prime Counting Function in Number Theory", in Volume 7 (2015). Containing ungrammatical and false claims like "So till now their is no formula for the prime counting function π(x) as you see from the end of 18th century till now" (completely ignoring the work of Meissel, Lehmer, Lagarias, Miller, Odlyzko, and others), this paper is a mess. Understanding why the paper is silly is a bit more involved, so I'll start by explaining one aspect of what makes a paper good.

A general principle about theorems is that they should be (within reason) as general as possible. For example, if you prove that if some property of a specific set S holds, then before publishing it you should think about what more general property S has that makes it possible to get the result. Here's a specific example: recently I saw a reddit post that pointed out that every prime p greater than or equal to 5 can be expressed as p = (24n+1)&half;, for some integer n. This is totally uninteresting, but the reason why it's uninteresting is that this property has basically nothing to do with primes at all! Rather, it is trivial fact that every number q that is relatively prime to 6 has the property that q2 ≡ 1 (mod 24), a fact that can instantly be verified by computing (6k+1)2 and (6k+5)2 and observing that k(k+1) is always even. Since every prime greater than or equal to 5 is relatively prime to 6, the result follows immediately. But, I emphasize again, the result is really about numbers relatively prime to 6, not primes. It captures basically nothing interesting about primes at all.

Now, in Abtan's paper, what is the silliness? He states the following formula for the prime-counting function π(x), which is the number of primes ≤ x. (For example, π(10) = 4.)

π(x) = (Σ2≤p≤xp + Σ2≤n<x π(n))/X.

Now, as stated, this formula contains two silly features. First, X is undefined; it should be x. (Where were the editors or referees for this paper?!?) Second, the formula is manifestly incorrect when x is not an integer (for example, try x = 2.5). So we shouldn't use x, because among mathematicians, x usually implies a real-valued variable. Let's use N instead.

With these two corrections, the formula becomes correct:

π(N) = (Σ2≤p≤Np + Σ2≤n<N π(n))/N for integers N ≥ 1.

Let's overlook the fact that the formula is completely useless for computing prime numbers or π(N), and instead focus on the formula itself. Remember the principle: try to figure out the class of sequences for which such a formula might hold. Well, let's try some interesting but completely unrelated sequence, like the squares.
Instead of π(N), we might define sqrt(N), the number of positive integer squares ≤ N.
Does a similar formula hold?

Yes! In fact, more or less exactly the same formula holds:

sqrt(N) = (Σ1≤i2≤Ni2 + Σ1≤n<N sqrt(n))/N for integers N ≥ 1.

How can this be? Well, the obvious answer is that Abtan's formula (for which he gave a long and complicated induction proof) has nothing to do with primes at all!

Let us generalize Abtan's formula and give a very, very simple proof of it. (It is often the case that if you generalize a theorem properly, it becomes easier to prove than a specific case might be.)

To generalize it, let S be any set of positive integers. S could be the prime numbers, or the positive square integers, or anything else. Let πS(n) denote the number of elements of S that are ≤ n. Then we claim that

πS(N) = (Σ1≤s≤N and s ∈ Ss + Σ1≤n<N πS(n))/N for integers N ≥ 1.

This has an easy proof by diagram! To see it, draw a histogram of the function πS(n) from
n = 1 to N. For example, for the primes and N = 12, this would look like

How about the boxes in the rectangle which are not colored in red? Well, the top row is all blank boxes
until the first prime hit in this row, which is 11. So there are 10 boxes. In the next row, there are all blanks until the first prime hit, which is 7. So there are 6 boxes. And so forth. So the total number of white boxes is Σ2≤p≤N (p - 1) (or, more generally, Σ1≤s≤N and s ∈ S (s - 1).) Thus we have proved

NπS(N) =
Σ1≤s≤N and s ∈ S (s - 1) +
Σ1≤n≤N πS(n).

This is the nice version of Abtan's formula. To get his formula, just add πS(N) to the left sum and subtract it from the right, then divide by N, to get

πS(N) =
(Σ1≤s≤N and s ∈ Ss +
Σ1≤n<N πS(n))/N.

So we see that Abtan's formula has nothing to do with primes at all, really.

Any competent referee would have seen this immediately. Congratulations, IJMR. You're officially a Silly Journal™.

Wednesday, September 02, 2015

I digitized these a long time ago, but I can't find any record that I posted about it! So here are some old issues of APL News, a newsletter about the computer language APL published from 1978 to 1982 by Ken Iverson. I contributed a little to it.